import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

# 从-0.5到0.5 200个样本点 闭区间  不是随机的  [:,np.newaxis]行列转换
x_data = np.linspace(-0.5,0.5,1000)[:,np.newaxis]
# 正态分布
noise = np.random.normal(0,0.02,x_data.shape)
# 二次曲线 +  高斯噪声
y_data = np.square(x_data)+noise

# 定义两个placeholder  NONE数量未知
x = tf.placeholder(tf.float32,[None,1])
y = tf.placeholder(tf.float32,[None,1])

# 构建神经网络 实现线性回归
# 点  10   点   神经网络结构
# 定义中间层
Weights_L1 = tf.Variable(tf.random_normal([1,10]))
biases_L1 = tf.Variable(tf.zeros([1,10]))
Wx_plus_b_L1 = tf.matmul(x,Weights_L1) + biases_L1
# 对比sigmoid和tanh两者导数输出可知，tanh函数的导数
# 比sigmoid函数导数值更大，即梯度变化更快，
# 也就是在训练过程中收敛速度更快。但是莫幂运算速度较慢
L1 = tf.nn.tanh(Wx_plus_b_L1)

# 定义输出层
Weights_L2 = tf.Variable(tf.random_normal([10,1]))
biases_L2 = tf.Variable(tf.zeros([1,1]))
Wx_plus_b_L2 = tf.matmul(L1,Weights_L2) + biases_L2
prediction = tf.nn.tanh(Wx_plus_b_L2)

#  二次代价函数
loss = tf.reduce_mean(tf.square(y-prediction))
# 梯度下降法
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

with tf.Session() as sess:
    # 变量初始化
    sess.run(tf.global_variables_initializer())
    for _ in range(2000):
        sess.run(train_step,feed_dict={x:x_data,y:y_data})

    # 获得预测值
    prediction_value = sess.run(prediction,feed_dict={x:x_data})
    plt.figure()
    plt.scatter(x_data,y_data)
    plt.plot(x_data,prediction_value,'r-',lw=5)
    plt.show()